Question

Consider the cubic function d(x)=2x−1−−−−−√3
and the square root function g(x)=2x+1−−−−−√
. Select the interval where the square root function has the lower estimated average rate of change.(1 point)

[1,5]


[0,4]


[3,7]


[2,6]

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Answer 1

g(x) = √(2x+1). Its average rate on [a,b] is (√(2b+1) − √(2a+1))/(b−a). Computing each:

- [1,5]: (√11 − √3)/4 ≈ 0.396
- [0,4]: (√9 − √1)/4 = 2/4 = 0.5
- [3,7]: (√15 − √7)/4 ≈ 0.307
- [2,6]: (√13 − √5)/4 ≈ 0.342

Smallest is [3,7].